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" Algorithmic methods in non-commutative algebra : "
by José L. Bueso, José Gomez-Torrecillas, Alain Verschoren.
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BL
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| Record Number
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776555
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b596552
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| Main Entry
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by José L. Bueso, José Gomez-Torrecillas, Alain Verschoren.
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| Title & Author
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Algorithmic methods in non-commutative algebra : : applications to quantum groups\ by José L. Bueso, José Gomez-Torrecillas, Alain Verschoren.
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| Publication Statement
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Dordrecht ; London : Springer, 2011
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| Series Statement
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Mathematical modelling. Theory and applications, v. 17
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(1 v).
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| ISBN
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9048163285
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: 9401702853
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: 9789048163281
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: 9789401702850
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| Notes
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Originally published: 2003.
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| Contents
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Introduction. 1: Generalities on rings. 1. Rings and ideals. 2. Modules and chain conditions. 3. Ore extensions. 4. Factorization. 5. Other examples. 6. Quantum groups. 2: Groebner basis computation algorithms. 1. Admissible orders. 2. Left Poincare-Birkhoff-Witt Rings. 3. Examples. 4. The Division Algorithm. 5. Groebner bases for left ideals. 6. Buchberger's Algorithm. 7. Reduced Groebner Bases. 8. Poincare-Birkhoff-Witt rings. 9. Effective computations for two-sided ideals. 3: Poincare-Birkhoff-Witt Algebras. 1. Bounding quantum relations. 2. Misordering. 3. The Diamond Lemma. 4. Poincare-Birkhoff-Witt Theorems. 5. Examples. 6. Iterated Ore Extensions. 4: First applications. 1. Applications to left ideals. 2. Cyclic finite-dimensional modules. 3. Elimination. 4. Graded and filtered algebras. 5. The omega-filtration of a PBW algebra. 6. Homogeneous Groebner bases. 7. Homogenization. 5: Groebner bases for modules. 1. Groebner bases and syzygies. 2. Computation of the syzygy module. 3. Admissible orders in stable subsets. 4. Groebner bases for modules. 5. Groebner bases for subbimodules. 6. Elementary applications of Groebner bases for modules. 7. Graded and filtered modules. 8. The omega-filtration of a module. 9. Homogeneous Groebner bases. 10. Homogenization. 6:Syzygies and applications. 1. Syzygies for modules. 2. Intersections. 3. Applications to finitely presented modules. 4. Schreyer's order. 5. Free resolutions. 6. Computation of Hom and Ext. 7: The Gelfand-Kirillov dimension and the Hilbert polynomial. 1. The Gelfand-Kirillov dimension. 2. The Hilbert function of a stable subset. 3.The Hilbert function of a module over a PBW algebra. 4. The Gelfand-Kirillov dimension of PBW algebras. 8: Primality. 1. Localization. 2. The Ore condition and syzygies. 3. A primality test. 4. The primality test in iterated differential operator rings. 5. The primality test in coordinate rings of quantum spaces. Index. References.
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| Subject
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Algorithms.
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Noncommutative algebras.
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Quantum groups.
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| LC Classification
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QA251.4B956 2011
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| Added Entry
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A Verschoren
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José Gómez-Torrecillas
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José Luis Bueso
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